Discrete Mathematics, Second Edition

Discrete mathematics focuses at its core on objects that can be separated and studied individually, in contrast to continuous objects such as functions or spaces in calculus or geometry. These objects may be graphs, sets, or numbers. The tools and techniques of discrete mathematics are distinct from those of other fields of mathematics, and often take on a combinatorial flavor, where we focus on counting objects.

The focus of the present book is to give an introduction to each of the topics of sets and logics, graphs, relations, functions, combinatorics, automata, and number theory. The book contains 210 exercises ranging in difficulty from easier to more challenging. Solutions are included at the end of each chapter for almost all the exercises. In some cases, only hints towards the solutions are provided. There are dozens of examples and figures that will aid in the comprehension of the material. A full solution manual, with detailed answers to all the problems in the text, is available as a separate book on Gumroad. Visit https://abonato.gumroad.com/l/nhuji to purchase the solutions manual.

In the second edition, I've added more examples and exercises. There are also now a number of resources at the end of each chapter to help you learn the material. There is a study guide for the topics of the chapter. You can this is as a quick, high-level summary of the topics in the chapter. I've also included a list of key questions about the chapter's content. If you can answer each of these, then you have fully grasped the material and are well-positioned to complete the exercises. There is a ten question quiz based on the material of the chapter, with short answers. There is also a brief history of the topics of the chapter, which is optional to read and can be a jumping off point for further study.